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   <div id="projectname">Calico
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   <div id="projectbrief">A visual-inertial calibration library designed for rapid problem construction and debugging.</div>
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<p>Primary calico namespace.  
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using&#160;</td><td class="memItemRight" valign="bottom"><b>Pose3d</b> = <a class="el" href="classcalico_1_1Pose3.html">Pose3</a>&lt; double &gt;</td></tr>
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ceres::Solver::Options&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacecalico.html#aaa1f3edabbaf4a92827f5340a76e37b6">DefaultSolverOptions</a> ()</td></tr>
<tr class="memdesc:aaa1f3edabbaf4a92827f5340a76e37b6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default solver options. <br /></td></tr>
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<tr class="memitem:a1bc1ca70bd6cfc6753dfef1ab61adff4"><td class="memTemplParams" colspan="2"><a id="a1bc1ca70bd6cfc6753dfef1ab61adff4"></a>
template&lt;typename T &gt; </td></tr>
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<tr class="memdesc:a1bc1ca70bd6cfc6753dfef1ab61adff4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a 3-vector to a skew-symmetric cross-product matrix. <br /></td></tr>
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<tr class="memitem:a68a61002300d80b0d403719b982400eb"><td class="memTemplParams" colspan="2"><a id="a68a61002300d80b0d403719b982400eb"></a>
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<tr class="memdesc:a68a61002300d80b0d403719b982400eb"><td class="mdescLeft">&#160;</td><td class="mdescRight">Converts a skew symmetric matrix back into a vector. <br /></td></tr>
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template&lt;typename T &gt; </td></tr>
<tr class="memitem:a98705a3b05fcd2103fa6823528c9cc7d"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacecalico.html#a98705a3b05fcd2103fa6823528c9cc7d">SmallAngleSin</a> (const T theta)</td></tr>
<tr class="memdesc:a98705a3b05fcd2103fa6823528c9cc7d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Fourth order Taylor expansion of sin(theta). <br /></td></tr>
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template&lt;typename T &gt; </td></tr>
<tr class="memitem:a68a6ed102c3feb3b52f5b9950a6b2bc4"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacecalico.html#a68a6ed102c3feb3b52f5b9950a6b2bc4">SmallAngleCos</a> (const T theta)</td></tr>
<tr class="memdesc:a68a6ed102c3feb3b52f5b9950a6b2bc4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Fourth order Taylor expansion of cos(theta). <br /></td></tr>
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template&lt;typename T &gt; </td></tr>
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<tr class="memdesc:aa4a4bab45cfce99938f0b261e5464547"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert axis-angle to rotation matrix. <br /></td></tr>
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<tr class="memitem:a4b5e83bfad1cc6b767ae5354d5d483c8"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a4b5e83bfad1cc6b767ae5354d5d483c8"><td class="memTemplItemLeft" align="right" valign="top">Eigen::Vector3&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacecalico.html#a4b5e83bfad1cc6b767ae5354d5d483c8">LnSO3</a> (const Eigen::Matrix3&lt; T &gt; &amp;R)</td></tr>
<tr class="separator:a4b5e83bfad1cc6b767ae5354d5d483c8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a405ed3df9c4ed8eebcabe5ec92d6717e"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a405ed3df9c4ed8eebcabe5ec92d6717e"><td class="memTemplItemLeft" align="right" valign="top">Eigen::Matrix3&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacecalico.html#a405ed3df9c4ed8eebcabe5ec92d6717e">ExpSO3Jacobian</a> (const Eigen::Vector3&lt; T &gt; &amp;phi)</td></tr>
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<tr class="memitem:a3e0aabf168db953b2b5903af43105582"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
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<tr class="memitem:a7d85e76032e1f2ab3267b64b3992b0d3"><td class="memTemplParams" colspan="2"><a id="a7d85e76032e1f2ab3267b64b3992b0d3"></a>
template&lt;typename T &gt; </td></tr>
<tr class="memitem:a7d85e76032e1f2ab3267b64b3992b0d3"><td class="memTemplItemLeft" align="right" valign="top">Eigen::Matrix3&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacecalico.html#a7d85e76032e1f2ab3267b64b3992b0d3">ExpSO3JacobianDot</a> (const Eigen::Vector3&lt; T &gt; &amp;phi, const Eigen::Vector3&lt; T &gt; &amp;phi_dot)</td></tr>
<tr class="memdesc:a7d85e76032e1f2ab3267b64b3992b0d3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute the time derivative of the Rodrigues formula manifold Jacobian. <br /></td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>MATCHER_P2</b> (PoseIsApprox, expected_pose, tolerance, &quot;&quot;)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>MATCHER_P</b> (PoseEq, expected_pose, &quot;&quot;)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>MATCHER_P</b> (EigenEq, expected_vector, &quot;&quot;)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>MATCHER_P2</b> (EigenIsApprox, expected_vector, tolerance, &quot;&quot;)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>MATCHER_P</b> (StatusIs, status, &quot;&quot;)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>MATCHER_P</b> (StatusCodeIs, status, &quot;&quot;)</td></tr>
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constexpr int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacecalico.html#a6db3636699bf6c8f6405547a35608b33">kLandmarkFrameId</a> = -1</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Primary calico namespace. </p>
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<h2 class="memtitle"><span class="permalink"><a href="#a3e0aabf168db953b2b5903af43105582">&#9670;&nbsp;</a></span>ExpSO3Hessian()</h2>

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          <td class="memname">std::vector&lt;Eigen::Matrix3&lt;T&gt; &gt; calico::ExpSO3Hessian </td>
          <td>(</td>
          <td class="paramtype">const Eigen::Vector3&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>phi</em></td><td>)</td>
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<p>Compute the manifold Hessian matrix of the Rodrigues formula, i.e.: </p><p class="formulaDsp">
\[ \mathbf{R}(\boldsymbol{\Phi}) = \exp\left(\left[\boldsymbol{\Phi}\right]_\times\right) = \mathbf{I} + \frac{\sin(\theta)}{\theta}\left[\boldsymbol{\Phi}\right]_\times + \frac{1-\cos(\theta)}{\theta^2} {\left[\boldsymbol{\Phi}\right]_\times}^2\\ \mathbf{H} = \frac{\partial^2 \exp\left(\left[\boldsymbol{\Phi}\right]_\times\right)} {\partial \boldsymbol{\Phi}^2} \]
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<h2 class="memtitle"><span class="permalink"><a href="#a405ed3df9c4ed8eebcabe5ec92d6717e">&#9670;&nbsp;</a></span>ExpSO3Jacobian()</h2>

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          <td class="paramname"><em>phi</em></td><td>)</td>
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<p>Compute the manifold Jacobian matrix of the Rodrigues formula, i.e.: </p><p class="formulaDsp">
\[ \mathbf{R}\left(\boldsymbol{\Phi}\right) = \exp\left( \mathbf{I} + \frac{\sin(\theta)}{\theta} \left[\boldsymbol{\Phi}\right]_\times + \frac{1 - \cos(\theta)}{\theta^2}{\left[\boldsymbol{\Phi}\right]_\times}^2 \right)\\ \frac{\partial \exp\left(\left[\boldsymbol{\Phi}\right]_\times\right)}{\partial \boldsymbol{\Phi}} = \mathbf{I} + \frac{1-\cos(\theta)}{\theta^2} \left[\boldsymbol{\Phi}\right]_\times + \frac{\theta-\sin(\theta)}{\theta^3} {\left[\boldsymbol{\Phi}\right]_\times}^2\\ \theta = \boldsymbol{\Phi}^T\boldsymbol{\Phi} \]
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<h2 class="memtitle"><span class="permalink"><a href="#a4b5e83bfad1cc6b767ae5354d5d483c8">&#9670;&nbsp;</a></span>LnSO3()</h2>

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          <td class="memname">Eigen::Vector3&lt;T&gt; calico::LnSO3 </td>
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          <td class="paramtype">const Eigen::Matrix3&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>R</em></td><td>)</td>
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<p>Convert rotation matrix to axis-angle. Algorithm pulled from this page: <a href="https://math.stackexchange.com/questions/83874/efficient-and-accurate-numerical-implementation-of-the-inverse-rodrigues-rotatio">https://math.stackexchange.com/questions/83874/efficient-and-accurate-numerical-implementation-of-the-inverse-rodrigues-rotatio</a> </p>

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